A Domain Decomposition Method Derived from the Primal Hybrid Formulation for 2nd Order Elliptic Problems

Abstract

We introduce a framework for FETI methods using ideas from the decomposition via Lagrange multipliers of H 0 1 (Ω) derived by Raviart-Thomas [17] and complemented with the detailed work on polygonal domains developed by Grisvard [11]. We compute the action of the Lagrange multipliers using the natural H 00 1/2 scalar product. Our analysis allows to deal with cross points and floating subdomains in a natural manner. We obtain that the condition number for the iteration matrix is independent of the mesh size and there is no need for preconditioning. This result improves the standard asymptotic bound for this condition number given by (1 + log(H/h))2 shown by Mandel-Tezaur in [14]. Numerical results that confirm our theoretical analysis are presented in [2] or [4].